# Best way convert transfer function to FIR filter without group delay if i have complex transfer function data

when i calculate acoustic transfer function, system identification using adaptive fir filtering is usually used and that have not tap/2 group delay maybe.

in simulation if i have complex number of transfer function. ifft cause Non causal term and i have to shift coefficient. and that make group delay.

the group delay is critical

What is the best way to make FIR filter without group delay?

Thank you

If you only need to correct the magnitude of the spectrum, design a minimum phase filter instead of a linear phase filter. By definition, minimum-phase is the best you can do. The group delay will not be zero, at least not at all frequencies, but it will be as small as it can be at every frequency.

The filter will also be causal.

If you need to fit both magnitude and phase, there is nothing you can do. If your target is non-causal, so will be your filter.

• when estimate acoustic transfer function, i know wiener filter has no group delay isn't it true? you mean if i fit both magnitude and phase. M/2 group delay is always??
– gg h
Commented Feb 23, 2022 at 9:28
• Sorry, I don't understand your question. Acoustic Transfer functions are complex i.e. they have a magnitude and a phase. Whether the phase matters or not depends on your application. For example, if you want to equalize a speaker, you can (mostly) disregard the phase. If you do arraying or noise cancellation you need to match the phase carefully. All causal filters have group delay, but typically it's dependent on frequency. I think what you are talking about as "group delay" is the bulk delay of a linear phase filter. There are plenty of other filter types out there than don't have bulk delay Commented Feb 23, 2022 at 10:33
• Thank you, please see this post dsp.stackexchange.com/questions/81403/…
– gg h
Commented Feb 23, 2022 at 12:53
• Thank you, please see this post dsp.stackexchange.com/questions/81403/… . for example when i convert Acoustic transfer function to fir filter from above method, M order fir filter have original phase delay (Acoustic transfer function)at each frequency bin and have some linear phase(fftshift, to make causal). linear phase(group delay) have M/2 delay. M/2 delay is not reasonable. Could you tell me how can i reduce M/2 delay?
– gg h
Commented Feb 23, 2022 at 12:58